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dc.contributor.authorBojilov, Asen
dc.contributor.authorCaro, Yair
dc.contributor.authorHansberg Pastor, Adriana
dc.contributor.authorNedyalko, Nevno
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.date.accessioned2013-06-12T13:07:19Z
dc.date.created2013-09
dc.date.issued2013-09
dc.identifier.citationBojilov, A. [et al.]. Partitions of graphs into small and large sets. "Discrete applied mathematics", Setembre 2013, vol. 161, núm. 13-14, p. 1912-1924.
dc.identifier.issn0166-218X
dc.identifier.urihttp://hdl.handle.net/2117/19540
dc.description.abstractLet GG be a graph on nn vertices. We call a subset AA of the vertex set V(G)V(G)kk-small if, for every vertex v∈Av∈A, deg(v)≤n−|A|+kdeg(v)≤n−|A|+k. A subset B⊆V(G)B⊆V(G) is called kk-large if, for every vertex u∈Bu∈B, deg(u)≥|B|−k−1deg(u)≥|B|−k−1. Moreover, we denote by φk(G)φk(G) the minimum integer tt such that there is a partition of V(G)V(G) into View the MathML sourcetk-small sets, and by Ωk(G)Ωk(G) the minimum integer tt such that there is a partition of V(G)V(G) into View the MathML sourcetk-large sets. In this paper, we will show tight connections between kk-small sets, respectively kk-large sets, and the kk-independence number, the clique number and the chromatic number of a graph. We shall develop greedy algorithms to compute in linear time both φk(G)φk(G) and Ωk(G)Ωk(G) and prove various sharp inequalities concerning these parameters, which we will use to obtain refinements of the Caro–Wei Theorem, Turán’s Theorem and the Hansen–Zheng Theorem among other things.
dc.format.extent13 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subject.lcshGraphs
dc.subject.otherkk-small set
dc.subject.otherkk-large set
dc.subject.otherkk-independence
dc.subject.otherClique number
dc.subject.otherChromatic number
dc.titlePartitions of graphs into small and large sets
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.identifier.doi10.1016/j.dam.2013.02.038
dc.description.peerreviewedPeer Reviewed
dc.rights.accessRestricted access - publisher's policy
local.identifier.drac12465493
dc.description.versionPostprint (published version)
dc.date.lift10000-01-01
local.citation.authorBojilov, A.; Caro, Y.; Hansberg, A.; Nedyalko, N.
local.citation.publicationNameDiscrete applied mathematics
local.citation.volume161
local.citation.number13-14
local.citation.startingPage1912
local.citation.endingPage1924


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